- 40
- 1
- Summary
- I've attached an image of a solved problem. Can somebody explain the steps in the yellow box? I don't understand how they got to that point from the previous steps.
That is the step that is bothering me. Can you explain why all values of a must be 0 except a1?I suspect it is the first step that is bothering you.
[tex] \sum_{n=1}^{\infty}a_n \sin(\frac{n \pi x}{2}) \sinh(\frac{n \pi}{2}) = \sin(\frac{\pi x}{2}) [/tex]
This is true for all values of x. The only way this can be true is for all of the [itex] a_n[/itex] to be zero except [itex]a_1[/itex]. Is this the step that is troubling you? After this, the rest follows pretty easily.
The functions [itex] \sin(\frac{n \pi x}{2})[/itex] are orthogonal functions on the interval (0,2). If I integrate:That is the step that is bothering me. Can you explain why all values of a must be 0 except a1?